BRACKETS AND EQUATIONS

BRACKETS

 

The terms enclosed in brackets are to be treated as a single number.

Thus a+(b-c) means that we have first to subtract c from b and then add the result to a.

a x (b + c) means that the sum of b and c is to be multiplied by a.

Removal of brackets

Brackets are more  changing the value of the expressions enclosed in them.

The value of an expression containing brackets remains unaltered even if we remove the brackets ,provided that these brackets are preceded by the positive sign.

 

In case of subtraction we can remove brackets preceded by the negative sign by changing the sign of every term in the brackets i.e. changing + into – and – into +.

Consider the four cases in general

1.a + ( b + c) =a+ b+ c      

2. a + ( b – c) = a+ b – c

3. a – ( b + c ) =a- b – c

4. a – ( b – c ) = a – b + c

These results are always true for all values of a, b and c.

Again , just as we can remove brackets , we can also enclose a number of terms in brackets.

If a number of terms are to be enclosed in brackets with the + sign placed before them, the sign of each term to be enclosed in them remains the same.

If the brackets have the – sign placed before them , the sign of each term to be enclosed in them must be changed from + into -, and – into +.

15 – ( 8 + 3 ) = 15 -11=4.

Multiplication

To multiply a bracketed expression by a number is to multiply each term of the expression by that number, and then to collect all the partial products together to get the final result.

           

 

The figure is a rectangle whose length is , say ( x+ y) cm and whose breadth is a cm.

Divide  the rectangle , as shown in the figure , into two smaller rectangles,one of which is x cm long and a cm broad, and the other , y cm long and a cm broad.

 The area of the whole rectangle is clearly a( x+ y) sq.cm; and this area is equal to the area of the first rectangle, ax sq.cm ,plus the area of the second rectangle ;a y sq.cm.

Thus a ( x + y ) = ax + a y.

 

Method of solving  a simple equation

1. Simplify both sides of the given equation by removing brackets if any.

2.Transpose all terms involving the unknown to one side ( left or right side whichever is convenient ) taking care to change the signs of the terms transposed.

3.Simplify each side by collecting like terms together.

4.Divide each side by the coefficient of the unknown quantity to get the value of the unknown quantity.

This value is the root of the given equation.